Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Access Right: Open AccessAuthor: search.filters.author.Şahan, Gökhan

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  • Conference Object
    Existence and Uniqueness of Solution for Discontinuous Conewise Linear Systems
    (Elsevier, 2020) Şahan, Gökhan
    In this study, we give necessary and sufficient conditions for well posedness of Conewise Linear Systems in 3-dimensional space where the vector field is allowed to be discontinuous. The conditions are stated using the subspaces derived from subsystem matrices and the results are compared with the existing conditions given in the literature. We show that even we don't have a fixed structure on system matrices as in bimodal systems, similar subspaces and numbers again determines well posedness. Copyright (C) 2020 The Authors.
  • Article
    Relaxation of Conditions of Lyapunov Functions
    (2021) Şahan, Gökhan
    In this study, stability conditions are given for nonlinear time varying systems using the classical Lyapunov 2nd Method and its arguments. A novel approach is utilized and so that uniform stability can also be proved by using an unclassical Lyapunov Function. In contrast with the studies in the literature, Lyapunov Function is allowed to be negative definite and increasing through the system. To construct a classical Lyapunov Function, we use a reverse time approach methodology for the intervals where the unclassical one is increasing. So we prove the stability using a new Lyapunov Function construction methodology. The main result shows that the existence of such a function guarantees the stability of the origin. Some numerical examples are also given to demonstrate the efficiency of the method we use.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    The Effect of Coupling Conditions on the Stability of Bimodal Systems in R3
    (Elsevier Ltd., 2016) Eldem, Vasfi; Şahan, Gökhan
    This paper investigates the global asymptotic stability of a class of bimodal piecewise linear systems in R3. The approach taken allows the vector field to be discontinuous on the switching plane. In this framework, verifiable necessary and sufficient conditions are proposed for global asymptotic stability of bimodal systems being considered. It is further shown that the way the subsystems are coupled on the switching plane plays a crucial role on global asymptotic stability. Along this line, it is demonstrated that a constant (which is called the coupling constant in the paper) can be changed without changing the eigenvalues of subsystems and this change can make bimodal system stable or unstable.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Well Posedness Conditions for Bimodal Piecewise Affine Systems
    (Elsevier Ltd., 2015) Şahan, Gökhan; Eldem, Vasfi
    This paper considers well-posedness (the existence and uniqueness of the solutions) of Bimodal Piecewise Affine Systems in ℝn. It is assumed that both modes are observable, but only one of the modes is in observable canonical form. This allows the vector field to be discontinuous when the trajectories change mode. Necessary and sufficient conditions for well-posedness are given as a set of algebraic conditions and sign inequalities. It is shown that these conditions induce a joint structure for the system matrices of the two modes. This structure can be used for the classification of well-posed bimodal piecewise affine systems. Furthermore, it is also shown that, under certain conditions, well-posed Bimodal Piecewise Affine Systems in ℝn may have one or two equilibrium points or no equilibrium points.